Connecting tables with zero-one entries by a subset of a Markov basis

Details Connecting tables with zero-one entries by a subset of a Markov basis Connecting tables with zero-one entries by a subset of a Markov basis

2009-08-31

arxiv.org/abs/0908.4461v2

in Algebraic Methods in Statistics and Probability II, Contemporary Mathematics, vol. 516, Amer. Math. Soc., Providence, RI, p

Mathematics

Statistics Theory

18 pages

Scientific paper

We discuss connecting tables with zero-one entries by a subset of a Markov basis. In this paper, as a Markov basis we consider the Graver basis, which corresponds to the unique minimal Markov basis for the Lawrence lifting of the original configuration. Since the Graver basis tends to be large, it is of interest to clarify conditions such that a subset of the Graver basis, in particular a minimal Markov basis itself, connects tables with zero-one entries. We give some theoretical results on the connectivity of tables with zero-one entries. We also study some common models, where a minimal Markov basis for tables without the zero-one restriction does not connect tables with zero-one entries.

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